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    "# 金融市场基础第5节课书面作业\n",
    "学号：114847\n",
    "\n",
    "**作业内容：**  \n",
    "1. X企业可以以4.5%进行固定利率借款，Libor+1.5%进行浮动利率借款。Y企业可以以5.5%固定利率借款，Libor+2%浮动利率借款。如果某金融机构设计一款互换产品给X和Y企业，如果X和Y企业分别分别可以节省20个base points的借款成本，则金融机构可以从中赚取多少个base points的利润？  \n",
    "2. 现在有一款利率互换产品，2年期限，半年付息一次，固定利率6%，浮动利率为Libor+50个基点，名义本金是10million，如果在第三个半年付息后Libor利率为5%，在第四个半年，净利息结算为多少？"
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   "cell_type": "markdown",
   "id": "cd5bb4fa",
   "metadata": {},
   "source": [
    "## 第1题\n",
    "X企业可以以4.5%进行固定利率借款，Libor+1.5%进行浮动利率借款。Y企业可以以5.5%固定利率借款，Libor+2%浮动利率借款。如果某金融机构设计一款互换产品给X和Y企业，如果X和Y企业分别分别可以节省20个base points的借款成本，则金融机构可以从中赚取多少个base points的利润？  \n",
    "\n",
    "答："
   ]
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   "source": [
    "从这题目来看，X在固定利率上有比较优势，Y在浮动利率上有比较优势。应该是X想借浮动利益贷款，Y想借固定利率贷款，才会有互换产品一说。在这种情况下可以，如果不采用互换产品，是X要以Libor+1.5%借款，Y要以5.5%贷款，总共要贷款利率为Libor+7%，如果采用互换产品，即用X的固定利率贷款给Y再加上Y的浮动利率借款给X，则总共的贷款利率为Libor+6.5%, 共节省利率0.5%，如果X和Y分别节省20个bp,即0.2%, 则还有0.1%利润节余，这0.1%就是金融机构可以从中赚取的得利润，即10个base points。"
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  },
  {
   "cell_type": "markdown",
   "id": "1129d71b",
   "metadata": {},
   "source": [
    "## 第2题\n",
    "现在有一款利率互换产品，2年期限，半年付息一次，固定利率6%，浮动利率为Libor+50个基点，名义本金是10million，如果在第三个半年付息后Libor利率为5%，在第四个半年，净利息结算为多少？  \n",
    "\n",
    "答："
   ]
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   "id": "1e310767",
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   "source": [
    "在第四个半年，对于固定利率而言，利息为:\n",
    "$$\n",
    "I_{fixed} = 10 \\times 6\\% = 0.6 \\; million\n",
    "$$"
   ]
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   "cell_type": "markdown",
   "id": "c811332b",
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   "source": [
    "对于浮动利率而言，利息为：\n",
    "$$\n",
    "I_{floating}=10 \\times (5+0.5)\\% = 0.55 \\; million\n",
    "$$"
   ]
  },
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   "cell_type": "markdown",
   "id": "57e25cf8",
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   "source": [
    "因此，净利息结算，对于一方来说是：$0.05\\; million$，而对于另一方来说是：$-0.05\\; million$。"
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